Advertisements
Advertisements
प्रश्न
Find the derivative of f (x) = 3x at x = 2
उत्तर
We have:
\[{f'(2) = \lim}_{h \to 0} \frac{f(2 + h) - f(2)}{h}\]
\[ = \lim_{h \to 0} \frac{3(2 + h) - 3(2)}{h}\]
\[ = \lim_{h \to 0} \frac{6 + 3h - 6}{h}\]
\[ = \lim_{h \to 0} \frac{3h}{h}\]
\[ = 3\]
APPEARS IN
संबंधित प्रश्न
Find the derivative of x–4 (3 – 4x–5).
Find the derivative of the following function (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):
(x + a)
Find the derivative of the following function (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):
(ax + b)n
Find the derivative of the following function (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):
`(sec x - 1)/(sec x + 1)`
Find the derivative of the following function at the indicated point:
\[\frac{x + 1}{x + 2}\]
(x + 2)3
x ex
Differentiate of the following from first principle:
x sin x
Differentiate each of the following from first principle:
sin x + cos x
Differentiate each of the following from first principle:
\[e^{x^2 + 1}\]
Differentiate each of the following from first principle:
\[e^\sqrt{2x}\]
Differentiate each of the following from first principle:
\[e^\sqrt{ax + b}\]
tan2 x
3x + x3 + 33
cos (x + a)
x3 ex
\[\frac{2^x \cot x}{\sqrt{x}}\]
x2 sin x log x
(x sin x + cos x) (x cos x − sin x)
(1 − 2 tan x) (5 + 4 sin x)
sin2 x
x5 (3 − 6x−9)
x−4 (3 − 4x−5)
Differentiate each of the following functions by the product rule and the other method and verify that answer from both the methods is the same.
(x + 2) (x + 3)
\[\frac{x \sin x}{1 + \cos x}\]
\[\frac{1 + 3^x}{1 - 3^x}\]
\[\frac{x^5 - \cos x}{\sin x}\]
Write the value of \[\lim_{x \to a} \frac{x f (a) - a f (x)}{x - a}\]
If \[\frac{\pi}{2}\] then find \[\frac{d}{dx}\left( \sqrt{\frac{1 + \cos 2x}{2}} \right)\]
Write the value of \[\frac{d}{dx}\left( x \left| x \right| \right)\]
If f (x) = \[\frac{x^2}{\left| x \right|},\text{ write }\frac{d}{dx}\left( f (x) \right)\]
Mark the correct alternative in of the following:
If \[y = \frac{\sin\left( x + 9 \right)}{\cos x}\] then \[\frac{dy}{dx}\] at x = 0 is
Let f(x) = x – [x]; ∈ R, then f'`(1/2)` is ______.
